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In this paper, a formulation of the Helmholtz equation for three dimensional sound propagation in a moving inhomogeneous medium in cylindrical coordinates is derived. Based on this formulation, a three dimensional parabolic equation (PE) is constructed. This PE can be used to model sound propagation in an inhomogeneous arbitrary moving medium. The method is used here to simulate three dimensional outdoor sound propagation above a rigid flat ground surface. The numerical results for two simple wind cases are presented and compared with analytical results to validate the methodology. Examples of propagation problems with more complicated wind are then included to demonstrate the importance of including the wind velocity directly in the PE method.
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Cheng et al. (2009) studied this question.
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